scholarly journals Nonlinear Differential Problem with p-Laplacian and via Phi-Hilfer Approach: Solvability and Stability Analysis

2021 ◽  
Vol 1 (2) ◽  
pp. 164-181
Author(s):  
Hamid Beddani ◽  
Moustafa Beddani ◽  
Zoubir Dahmani
Keyword(s):  
Stability Analysis ◽  
General Class ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Differential Problem

This paper we consider a study of a general class of nonlinear singular fractional DEs with p-Laplacian for the existence and uniqueness solution and the Hyers-Ulam (HU) stability. result via ϕ−Hilfer derivative is studied. Then, an existence of one solution is investigated. Some illustrative examples are discussed at the end.

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

scholarly journals One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model

2020 ◽  
Vol 15 ◽  
pp. 25
Author(s):  
Ivan Gudoshnikov ◽  
Mikhail Kamenskii ◽  
Oleg Makarenkov ◽  
Natalia Voskovskaia
Keyword(s):  
Stability Analysis ◽  
Cyclic Loading ◽  
Finite Time ◽  
Stability Result ◽  
Stress Evolution ◽  
Time Stability ◽  
Elastoplastic Model ◽  
Finite Time Stability ◽  
Sweeping Processes ◽  
Simple Network

We offer a finite-time stability result for Moreau sweeping processes on the plane with periodically moving polyhedron. The result is used to establish the convergence of stress evolution of a simple network of elastoplastic springs to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the vertices of the polyhedron makes finite-time stability impossible.

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

scholarly journals A NOTE ON VARIATIONAL SOLUTIONS TO SPDE PERTURBED BY GAUSSIAN NOISE IN A GENERAL CLASS

2009 ◽  
Vol 12 (02) ◽  
pp. 353-358
Author(s):  
MICHAEL RÖCKNER ◽  
YI WANG
Keyword(s):  
Hilbert Space ◽  
Gaussian Noise ◽  
Stochastic Partial Differential Equations ◽  
General Class ◽  
Existence And Uniqueness ◽  
Nonlinear Operators ◽  
Infinite Dimensional ◽  
Variational Solutions ◽  
Cylindrical Wiener Process ◽  
Monotonicity Conditions

This note deals with existence and uniqueness of (variational) solutions to the following type of stochastic partial differential equations on a Hilbert space [Formula: see text][Formula: see text] where A and B are random nonlinear operators satisfying monotonicity conditions and G is an infinite dimensional Gaussian process adapted to the same filtration as the cylindrical Wiener process W(t),t ≥ 0.

scholarly journals Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians

2019 ◽  
Vol 21 (01) ◽  
pp. 1750098 ◽  
Author(s):  
Andrea Davini
Keyword(s):  
Viscosity Solution ◽  
Viscosity Solutions ◽  
Parabolic Equations ◽  
General Class ◽  
Existence And Uniqueness ◽  
Quasilinear Equations ◽  
Uniqueness Of Solutions ◽  
Superlinear Growth ◽  
Lipschitz Estimates ◽  
Jacobi Equations

We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the gradient variable. The approach is mainly based on classical techniques for uniformly parabolic quasilinear equations and on the Lipschitz estimates provided in [S. N. Armstrong and H. V. Tran, Viscosity solutions of general viscous Hamilton–Jacobi equations, Math. Ann. 361 (2015) 647–687], as well as on viscosity solution arguments.

scholarly journals Existence and Uniqueness with Ulam Stability study of the solution for a class of Caputo fractional integro-differential equation with mixed conditions

2021 ◽  
Author(s):  
ABDELLOUAHAB Naimi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Stability Study ◽  
Ulam Stability ◽  
Differential Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Stability Results

In this article we show the existence, uniqueness and Ulam stability results of the solution for a class of a nonlinear Caputo fractional integro-differential problem with mixed conditions. we use three fixed point theorems to proof the existence and uniqueness results. By the results obtained, the reasons for the Ulam stability are verified. An example proposed to illustrate our main results.

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